Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22558981 | C2 | semidirect |
| 4. #22558864 | C2 | semidirect |
| 5. #22558772 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 179. #1286 | D67 | semidirect |
| 180. C67 | #10468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570008 | 2 |
| #22560216 | 2 |
| #22558981 | 2 |
| #22558864 | 2 |
| #22558772 | 2 |
| #22558529 | 2 |
| C67×#1286 | 2 |
| #10468 | 67 |